six steps in regression analysis by hasan nagra econometrics sir atif notes

7/28/2019 six steps in regression analysis by hasan nagra econometrics sir atif notes

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3-1 2011 Pearson Addison-Wesley. All rights reserved.

Steps in Applied

Regression Analysis

The first step is choosing the dependent variable this step isdetermined by the purpose of the research (see Chapter 11 fordetails)

After choosing the dependent variable, its logical to follow thefollowing sequence:

1. Review the literature and develop the theoretical model

2. Specify the model: Select the independent variables and thefunctional form

3. Hypothesize the expected signs of the coefficients4. Collect the data. Inspect and clean the data

5. Estimate and evaluate the equation

6. Document the results


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Step 1: Review the Literature and

Develop the Theoretical Model

Perhaps counter intuitively, a strong theoretical foundation

is the best start for any empirical project

Reason: main econometric decisions are determined by theunderlying theoretical model

Useful starting points:

Journal of Economic Literature or a business oriented publication of

abstracts

Internet search, including Google Scholar

EconLit, an electronic bibliography of economics literature (for more

details, go to www.EconLit.org)


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Step 2: Specify the Model: Independent

Variables and Functional Form

After selecting the dependent variable, thespecification of a model involves choosing thefollowing components:

1. the independent variables and how they should bemeasured,

2. the functional (mathematical) form of the variables,and

3. the properties of the stochastic error term


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Step 2: Specify the Model:

Independent Variables and

Functional Form (cont.)

A mistake in any of the three elements results in a specification error

For example, only theoretically relevant explanatory variables should

be included

Even so, researchers frequently have to make choicesalso denoted

imposing theirpriors

Example:

when estimating a demand equation, theory informs us that prices of

complements and substitutes of the good in question are importantexplanatory variables

But which complementsand which substitutes?


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Step 3: Hypothesize the Expected

Signs of the Coefficients

Once the variables are selected, its important to

hypothesize the expected signs of the regression

coefficients

Example: demand equation for a final consumption good

First, state the demand equation as a general function:

(3.2)

The signs above the variables indicate the hypothesized

sign of the respective regression coefficient in a linear

model


7/303-6 2011 Pearson Addison-Wesley. All rights reserved.

Step 4: Collect the Data & Inspect

and Clean the Data

A general rule regarding sample size is the moreobservations the better

as long as the observations are from the same general

population!

The reason for this goes back to notion ofdegrees offreedom (mentioned first in Section 2.4)

When there are more degrees of freedom:

Every positive error is likely to be balanced by a negative error(see Figure 3.2)

The estimated regression coefficients are estimated with agreater deal ofprecision



Figure 3.1 Mathematical Fit of a

Line to Two Points



Figure 3.2 Statistical Fit of a Line

to Three Points



Step 4: Collect the Data & Inspect

and Clean the Data (cont.)

Estimate model using the data in Table 2.2 to get:

Inspecting the dataobtain a printout or plot (graph)

of the data

Reason: to look foroutliers

An outlier is an observation that lies outside the range of the rest of

the observations

Examples:

Does a student have a 7.0 GPA on a 4.0 scale?

Is consumption negative?



Step 5: Estimate and Evaluate

the Equation

Once steps 14 have been completed, the estimation part

is quick

using Eviews orStata to estimate an OLS regression takes less

than a second!

The evaluation part is more tricky, however, involving

answering the following questions:

How well did the equation fit the data?

Were the signs and magnitudes of the estimated coefficients asexpected?

Afterwards may add sensitivity analysis (see Section 6.4

for details)


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Step 6: Document the Results

A standard format usually is used to present estimated

regression results:

(3.3)

The number in parentheses under the estimated coefficient

is the estimated standard errorof the estimatedcoefficient, and the t-value is the one used to test the

hypothesis that the true value of the coefficient is different

from zero (more on this later!)


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Case Study: Using Regression Analysis

to Pick Restaurant Locations

Background:

You have been hired to determine the best location

for the next Woodys restaurant (a moderately priced,24-hour, family restaurant chain)

Objective:

How to decide location using the six basic steps ofapplied regression analysis, discussed earlier?


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Step 1: Review the Literature and

Develop the Theoretical Model

Background reading about the restaurant industry

Talking to various experts within the firm

All the chains restaurants are identical and located insuburban, retail, or residential environments

So, lack of variation in potential explanatory variables to help

determine location

Number of customers most important for locational decision

Dependent variable: number of customers (measured by

the number of checks or bills)


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Variables and Functional Form

More discussions with in-house experts

reveal three major determinants of sales:

Number of people living near the location

General income level of the location

Number of direct competitors near the location


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Variables and Functional Form (cont.)

Based on this, the exact definitions of the independentvariables you decide to include are:

N = Competition: the number of direct competitors within a two-mile radius of the Woodys location

P = Population: the number of people living within a three-mileradius of the location

I = Income: the average household income of the populationmeasured in variable P

With no reason to suspect anything other than linearfunctional form and a typical stochastic error term,thats what you decide to use


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Step 3: Hypothesize the Expected

Signs of the Coefficients

After talking some more with the in-house

experts and thinking some more, you

come up with the following:

(3.4)


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Step 4: Collect the Data &

Inspect and Clean the Data

You manage to obtain data on the dependent and

independent variables for all 33 Woodys restaurants

Next, you inspect the data

The data quality is judged as excellent because:

Each managermeasures each variable identically

Allrestaurants are included in the sample

All information is from the sameyear

The resulting data is as given in Tables 3.1 and 3.3 in the

book (using Eviews and Stata, respectively)


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Step 6: Document the Results

The results summarized in Equation 3.5

meet our documentation requirements

Hence, you decide that theres no need to

take this step any further


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Table 3.1a

Data for the Woodys Restaurants Example

(Using the Eviews Program)


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Table 3.1b




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Table 3.1c




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Table 3.2a

Actual Computer Output



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Table 3.2b




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Table 3.3


(Using the Stata Program)


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Table 3.3b




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Table 3.4a




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Table 3.4b




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3 29

Key Terms from Chapter 3

The six steps in applied regression analysis

Dummy variable

Cross-sectional data set

Specification error

Degrees of freedom

six steps in regression analysis by hasan nagra econometrics sir atif notes

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